No, the settings in the Save dialog and Workflow Options dialog are maintained separately. The reason is that the Workflow Options settings largely governs what happens to the image when you open it in Photoshop (e.g., for further processing), whereas the Save dialog's settings dictate what happens when you save it to disk (e.g., for web, for printing, for sending to a lab, etc.).

It is reasonably common to want these to be different settings, e.g., a full-resolution image as Adobe RGB or ProPhoto for opening into Photoshop (via Workflow Options), but saving a downsampled JPEG with output sharpening in sRGB for the web (via Save dialog).

A tip here is that both the Workflow Options and Save dialogs support presets, which enables you to switch settings quickly depending on your workflow needs.